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The inclusive cross sections of W$^+$, W$^-$, and Z boson production from 34different measurements performed in proton-(anti)proton collisions atcenter-of-mass energies $\sqrt{s}$ = 1.8--13 TeV, are compared to perturbativeQCD calculations at next-to-next-to-leading-order (NNLO) accuracy with foursets of parton distributions functions (CT14, HERAPDF2.0, MMHT14, and NNPDF3.0PDFs) and varying values of the strong coupling constant at the Z mass pole,$\alpha_s(m_Z)$. The data-theory agreement is good within the experimental andtheoretical uncertainties, with the CT14 and MMHT14 parton densities providingthe most overall consistent description of all cross section data. A value of$\alpha_s(m_Z) = 0.1188^{+0.0019}_{-0.0013}$ is extracted from a combined fitof the 28 experimental LHC measurements to the corresponding NNLO theoreticalpredictions obtained with the MMHT14 PDF set, which provides the most robustand stable QCD coupling extraction of this analysis.

Strong coupling $\alpha_s(m_Z)$ extraction from a combined NNLO analysis of inclusive electroweak boson cross sections at hadron colliders